A136223 Column 2 of triangle A136220; also equals column 0 of U^3 = A136236 where U = A136228.

1, 3, 21, 208, 2637, 40731, 742620, 15624420, 372892266, 9959561867, 294465305959, 9551090908795, 337297690543923, 12886076807637021, 529624555043780909, 23305654066781507361, 1093356525580359412557

Offset: 0

Author

Paul D. Hanna, Dec 25 2007

Keywords

• nonn

Comments

P = A136220 is a triangular matrix where column k of P^3 equals column 0 of P^(3k+3) such that column 0 of P^3 equals column 0 of P shift one place left.

Crossrefs

Cf. A136220 (P), A136228 (U), A136236 (U^3); other columns of P: A136221, A136222, A136224.

Programs

PARI

{a(n)=local(P=Mat(1),U,PShR);if(n==0,1,for(i=0,n+1, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#U,P[r,c], (U^c)[r-c+1,1]))));P[n+3,3])}